Environ. Sci. Technol. 2006, 40, 7828-7833
On-Road Heavy-Duty Diesel Particulate Matter Emissions Modeled Using Chassis Dynamometer Data TOM KEAR AND D. A. NIEMEIER* Department of Civil and Environmental Engineering, One Shields Avenue, University of California, Davis 95616
This study presents a model, derived from chassis dynamometer test data, for factors (operational correction factors, or OCFs) that correct (g/mi) heavy-duty diesel particle emission rates measured on standard test cycles for real-world conditions. Using a random effects mixed regression model with data from 531 tests of 34 heavyduty vehicles from the Coordinating Research Council’s E55/E59 research project, we specify a model with covariates that characterize high power transient driving, time spent idling, and average speed. Gram per mile particle emissions rates were negatively correlated with high power transient driving, average speed, and time idling. The new model is capable of predicting relative changes in g/mi on-road heavy-duty diesel particle emission rates for realworld driving conditions that are not reflected in the driving cycles used to test heavy-duty vehicles.
1. Introduction Diesel exhaust particulate matter (diesel PM) was identified as carcinogenic in animal tests as early as 1955 (1). Subsequent epidemiological studies of railroad workers were among the first to report evidence of carcinogenetic risk (2-5). Significant public health questions related to diesel PM have grown since the adoption of the national ambient air quality standard for particulate matter smaller than 2.5 µm in aerodynamic diameter (6). There are well documented concerns regarding diesel PM carcinogenic risks (7-13). In addition, although improved fuel and engine technologies have dated some of the earlier work, there is a growing body of literature linking fine particulate matter pollution to increased morbidity and mortality (14-16), cardiovascular disease and asthma (17-20), and DNA deletions (21) which in turn can lead to heritable DNA mutations (22, 23). As much as 70% of the total air toxic carcinogenic risk in the Los Angeles area has been attributed to diesel PM (24), and onroad heavy-duty diesel vehicles are a significant, if not predominate source (24). Designing transportation projects that minimize risk from diesel PM necessitates a better understanding of how gram per mile (g/mi) emissions vary by speed and facility type, where variability is defined as the normalized change in g/mi emissions as operating conditions change. Modeling variability is equivalent to modeling emissions, as long as a reference emission rate is known. Emission factor models use this principal, applying correction factors to a base emission rate, where the correction factors account for * Corresponding author phone: (530)752-8918; fax: (530)752-7872; e-mail:
[email protected]. 7828
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observed variations (e.g., speed correction factors, fuel correction factors, and temperature correction factors). The literature contains five basic methods that attempt to model diesel PM variability using laboratory emissions test data. Additionally, ambient diesel PM concentrations near roadways have been used to infer emissions rates from on-road heavy-duty vehicles. None of these existing methods are suitable for designing or evaluating transportation projects. Laboratory-based emission rates have been generally modeled as functions of speed, power, and/or acceleration using one of five methods: (1) assuming emissions are related to speed; (2) assuming emissions are related to power; (3) as a function of modal characteristics; (4) assuming emissions are related to power transients; and (5) as a linear combination of emissions data from several different tests. The first approach attempts to fit a (speed correction factor) curve through points defined by the average speed of various chassis dynamometer tests and their corresponding emission rates (typically in units of grams per mile or kilometer). The generalizability of this approach is limited by the lack of real world activity reflected in the available driving schedules (25), and those cycles that capture real world driving characteristics were constructed to represent trips at a given average speed, rather than performance on individual road segments (25, 26). Trip based speed correction factors, used in California’s emission factor model (EMFAC) (27, 28) and in a few models with narrow applications (e.g., refs 29-32), have been found unacceptable for modeling on-road heavyduty diesel PM emissions (33). There are two variations on the second approach relating diesel PM to power. U.S. EPA’s emission factor model, MOBILE, uses engine certification test data, combined with estimates of power consumption to estimate emission rates (35-39). For diesel PM, MOBILE does not attempt to adjust these emissions for variation in speed. The second variation fits a curve through points defined by positive kinetic energy (PKE) and the corresponding emission rates (similar to the speed correction approach). Regressions of on-road heavyduty diesel PM against PKE show a strong positive correlation, but there are confounding effects associated with power transients (40, 41, 43). The third approach uses modal activity data, binning emissions by speed and acceleration. The mean emission rate from each bin (typically in grams per second) is then used as an emissions estimate for driving conducted under corresponding conditions. This approach has been implemented by disaggregating diesel PM data using real-time CO measurements (44). One of the limitations of this method is that there are no functional relationships to aid in the design or evaluation of transportation projects. The fourth approach, modeling diesel PM as a function of power transients, is based on observations that soot emissions are better corralled with transients in fuel injection rates than with absolute fuel use (41, 45). This approach has been applied with some success in modeling diesel PM as a function of the rate of change in horse power summed over acceleration events (“severity”) (46), which is perhaps the best functional relationship between vehicle activity and diesel PM emissions. However, the model likely omits other variables that are also important. The last method involves representing diesel PM emissions on one test cycle as a weighted combination of the emissions generated from other test cycles. The weights are found by specifying parameters on the first cycle (i.e., PKE and speed) as linear combinations of those parameters on the other cycles (47). The results for NOx and CO2 are promising; 10.1021/es060177e CCC: $33.50
2006 American Chemical Society Published on Web 11/17/2006
however, to date, the approach has not worked as well for diesel PM (47). The availability of real-time diesel PM measurements is limited. While the tapered element oscillating microbalance (TEOM) and nephelometer are available to make real-time measurements, the data are often difficult to interpret. TEOM data have shown the best correlation to filter-based measurements (48); however, mechanical vibration, evaporation, and condensation of semivolatile compounds and water on the filter all add noise to these data (46). Axial dispersion of pollutants in the exhaust system and the difficulties in precisely aligning real-time vehicle activity to real-time TEOM results (33, 43, 49-51) also make interpretation difficult. With this study, we present a new approach for measuring the variation in on-road heavy-duty diesel PM emissions using a measure of power transients, as suggested above (46) low power (near idle) operation and average speed. Comparisons shown in the Supporting Information qualitatively suggest that the proposed model improve the accuracy of estimates and better defines the functional relationships between the observed emission rates and observed activity.
2. Proposed Model We use a mixed linear model to estimate normalized emissions rates as a function of intensity (a measure of high power transient driving), time spent idling, and average speed. Mixed or random effects models include fixed effect coefficients similar to traditional regression models as well as coefficients that are themselves a random variable typically distributed normally with a mean value of zero. Each subject, or vehicle in this case, takes on a specific realization of the random variable, and the probability of that realization occurring is included in the likelihood computations. An example of a mixed model would be one that might be used to estimate the height of children based on their ages. Each child in the study would have a slightly different mean growth rate over time. The overall mean growth rate would be captured by the fixed effect, and each child’s perturbation from the overall mean growth rate would be captured by a subject-specific realization of the random coefficient. The random component captures the unobserved heterogeneity of covariates between the subjects (children in this example, vehicles for this study) in longitudinal and repeated measure data. In eq 1, we specify our random effects linear model with normalized emissions rates estimated as a function of the key variables
ln(Yi,j,k) ) β(1)i(X(1)i,j,k)(X(3)i) + β(2)i(X(2)i,j,k)(X(3)i) + β(3) + γ(1)j(Z(1)i,j,k)(Z(2)j) + γ(2)j(Z(2)j) + i,j,k (1) where i ) index for technology group (i ) 1-9), j ) index for engine (j ) 1-43), k ) index for tests (k ) 1-531 for the final model and k ) 1-438 for the specification test model), Yi,j,k ) operational correction factor (OCF), X(1)i,j,k ) observed log hours per mile, X(2)i,j,k ) observed log intensity per mile, X(3)i ) 1 if technology ) i; 0 otherwise, Z(1)i,j,k ) random covariate: log seconds of idle per mile, Z(2)j ) 1 if engine ) j; 0 otherwise, β(1)i ) model coefficients quantifying the relation between emissions and time required to travel one mile (hours per mile), β(2)i ) model coefficients quantifying the relation between emissions and intensity (acceleration*HP w/ acceleration in mph/s), β(3) ) intercept (does not vary with technology), γ(1)j ) random model coefficient (for ln (seconds of idle per mile +1)), γ(2)j ) random intercept, and i,j,k ) error term (i.e., the residual). In eq 1, we use a log transformation because emission rates are constrained to nonzero values, and, when transformed, the emission rates are approximately normally
TABLE 1. Technology Group Definitions technology group
engine model years
1 2 3 4 5 6 7 8 9
model year < ) 1973 1974 < ) model year < ) 1978 1979 < ) model year < ) 1983 1984 < ) model year < ) 1987 1988 < ) model year < ) 1990 1991 < ) model year < ) 1993 1994 < ) model year < ) 1997 1998 < ) model year < ) 2002 2003 < ) model year
distributed. Emission rate data were normalized using the same vehicle’s emission rate from the heavy-duty urban dynamometer driving cycle (UDDS) test, with an inertial weight of 56 000 lbs. Because normalized rates are used, the results from the model represent a correction factor rather than an absolute emission rate. Similar correction factors in the literature would include speed correction factors and cycle correction factors. The new correction factor is not based on speed, nor does it use cycle as an independent variable. Thus, it can be thought of as an “operational correction factor” (OCF), adjusting for variations in the transient nature of the vehicle’s operation. The OCF is the observed on-road heavy-duty diesel PM emission rate from a test (in grams per mile) divided by the observed diesel PM emission rate from the same vehicle on the UDDS test cycle with a 56 000 lbs inertial weight. When more than one 56 000 lbs UDDS test was available for a given vehicle, the average of the observed emission rates was used. There is always some information lost in averaging, however, because the averaged UDDS results are only used in the denominator when normalizing, the test for variability will not be affected. Technology groups (Table 1) were used to pool engine model years required to meet the same certification standards. The proposed model specification has independent variables of the natural log of hours per mile, X(1)i,j,k, calculated by first inverting the average vehicle speed during the test and then taking the natural logarithm, and intensity, X(2)i,j,k, which is intended to capture the influence of transient driving activity. Intensity is estimated as a two-step process that requires the use of continuous (second-by-second) speed and power data (both of which are available in our data). First a raw measure of intensity is calculated by multiplying second-by-second horsepower and acceleration whenever both are positive and then summing that over the entire drive cycle. Intensity per mile is then estimated by dividing the raw intensity by the test length and adding a value of one (to avoid taking the log of zero), resulting in units of HP miles per hour per second. Each of the i technology groups are allowed to take on a unique value of the β(2)i regression coefficient. The third term in the model is an intercept term that does not vary with technology group. The random component isolates vehicle-specific correlation caused by unobserved parameters such as idle speed and auxiliary loads. We know from previous studies that both vehicle-to-vehicle and multiple tests on the same vehicle can vary substantially (45); the random component allows us to capture this effect. The log of (seconds of idle per mile) is also a random independent variable. Seconds of idle per mile is derived by summing the number of seconds with speeds between -1 mph and 1 mph, dividing that number by the distance traversed in miles, and then adding one (to avoid taking the log of zero).
3. Chassis Dynamometer Data We specified the model using 531 chassis dynamometer tests conducted on 34 vehicles during phase 1 and “phase 1.5” of VOL. 40, NO. 24, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 2. Test Cycle Statisticsa all 6 cycles used for the final model 4 cycles used to fit specification test models cruise3
Trans3
AC5080
2 cycles used to examine specification model results UDDS
creep34
HHDDT-s
Speed (MPH) mean SD
39.7 0.6
14.3 0.6
mean SD
9.1 0.6
50.9 4.5
36.5 0.7
18.7 0.5
1.8 0.1
49.0 1.4
925.1 44.4
6.1 0.8
Idle (Seconds per Mile) 5.1 0.4
63.6 3.7
Intensity (HP MPH/S2) mean 1352 StD 398
8868 2255
4052 744
6893 1168
4011 1220
2700 635
OCF mean SD
0.41 0.23
1.45 0.65
0.67 0.16
1.00 0.05
2.32 1.44
0.59 0.33
a Means and standard deviations refer to the mean of mean test speed for all tests on a given cycle and the standard deviation of the mean test speed for each of the tests on a given cycle.
the Coordinating Research Council E55/E59 study (62-64). All of the test vehicles were heavy heavy-duty trucks/trucktractors; the earliest engine model year was 1973, and the newest engine model year was 2003. Six of 34 vehicles had repairs made to them, and the pre- and postrepair tests were treated as tests on different vehicles (i.e., the 34 vehicles + repairs are treated as 43 unique vehicles). The E55/E59 study contained continuous (second-bysecond) speed and power data from 8 different test procedures; we used the results from the following six cycles: (1) EPA’s schedule D (UDDS); (2) the Australian AC5080; (3) CARB transient; (4) CARB cruise cycles; (5) the HHDDT-S cycle (a shortened version of the CARB high-speed cruise cycle), and (6) the creep34 cycle (four creep3 cycles backto-back separated by a sharp acceleration to about 8 mph). The results from individual creep3 tests and the idle tests are not used. We draw a distinction between idle tests, which contain only idle, and periods of idle that occur inside a transient cycle; periods of idle embedded within otherwise transient tests are used in our modeling. The dynamometer cycles and a detailed vehicle-dynamometer test matrix is provided in the Supporting Information. Table 2 provides the average speed, idle time, intensity, and OCF (normalized diesel PM) for each cycle. The creep34 cycle has a lower mean speed and contains more seconds of idle per mile, and its normalized on-road heavy-duty diesel PM emission rates are higher than the other test cycles. In contrast, the HHDDT-S cycle has the highest mean speed and almost no idle activity and is among the lowest normalized on-road heavy-duty diesel PM emission rates. These two cycles in effect bound the characteristics of the truck activity and emissions contained in the data set.
4. Results To fit the model, we divided the 531 chassis dynamometer tests from the CRC E55/E59 data into two data subsets. The first subset contained data from 438 tests conducted on the cruise3, trans3, AC5080, and UDDS chassis dynamometer driving cycles, and the second subset contained 93 tests performed using the creep34 and HHDDT-S chassis dynamometer driving cycles. We specified the model using the first subset of data, testing the model using the second subset of data. In order to identify any serious specification errors, we specified the model using relatively moderate cycles and then evaluated the model’s suitability when extrapolating to more extreme cycles. Once our model specification was 7830
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FIGURE 1. Observed vs predicted on-road heavy-duty normalized diesel PM emission rates from the specification test model (note: predicted rates based on fixed effects only). considered acceptable, we re-estimated the model using the full data set, which increases the precision of the estimated coefficients. In this section we begin by presenting some interesting findings from the specification analysis. We then conclude with a presentation of the final model, which was specified using the full data. Findings from the Specification Analysis. During our specification analysis we calculated the OCFs for the smaller data set (N ) 93) using only the fixed effects and compared them to the normalized g/mi emission rates observed directly from the laboratory measurements (Figure 1). Ideally, the predicted versus observed data should follow a line with slope one and intercept zero. We then compared the basic model specification to several other model specifications (e.g., replacing intensity first with severity and then PKE). The goal of this comparison was to check if the proposed intensity variable offered advantages over severity and PKE, which are already well-established in the literature. For both comparisons, the intensity model provided a better fit than either PKE or severity. We also compared the eq 1 model specification against the severity model proposed by Yanowitz et al. (46) and the modal model developed for TRANSIMS (44). We had to reduce the smaller data subset from 93 to 85 chassis dynamometer tests because the modal model developed for TRANSIMS does not encompass the entire range of engine model years represented in the CRC E55/E59 data set. The severity model from the literature is a simple linear model (i.e., g/mi emissions are a function of severity); we found that a log-log transformation fit the data better (eq 2) and used this model for comparison to our proposed model
ln(Yi,j,k) ) β(1)i(X(1)i,j,k)(X(2)i) + β(2)i(X(2)i) + i,j,k
(2)
where i ) index for technology group (i ) 1-9), j ) index for engine (j ) 1-43), k ) index for tests (k ) 1-531 or k ) 1-438 when comparing to the TRANSIMS modal model), Yi,j,k ) observed normalized PM emission rate, X(1)i,j,k ) observed log severity per mile, X(2)i ) an indicator variable, 1 if technology ) k, 0 otherwise, β(1)i β(2)i ) model coefficients quantifying the relation between emissions and activity, and i,j,k ) error term (i.e., the residual associated with test k). The first coefficient (β(1)i) has a unique value for each of the nine groups to control for the effect of severity by
TABLE 3. Test of Fixed Effects for the Proposed Model. Part I: F Statistics effect
numerator DF
denominator DF
F value
Pr > |t|
β(1)i β(2)i β(3)
9 9 1
427 427 42
36.51 86.05 236.81
